Paul Ryan hammered President Barack Obama's health care law Wednesday, stressing that he plans to use the early days of Donald Trump's presidency to "fix" the insurance system.

"You have to remember this law is getting much worse. It is what actuaries say, 'Entering a death spiral.' High, high premiums increase, high deductibles, no choices. We have to fix this problem," the House speaker told CNBC's "Squawk Box."

President-elect Donald Trump campaigned on a pledge to "repeal and replace" the law, known as Obamacare. He seized on rising premiums under the plan, which has broadly expanded health coverage in the United States.

Katie Kramer | CNBC

Speaker of the House Paul Ryan.

Ryan and his House GOP colleagues have tried numerous times to repeal the law but were never able to during Obama's tenure. With Trump's surprise win, Republicans are set to control Congress in addition to the White House, putting Obamacare repeal and other GOP priorities within reach.

The Wisconsin Republican said he wanted to stress that a "reasonable" transition period would follow a repeal, "so we're not pulling the rug out from under people midstream." He said Americans are concerned about losing their coverage immediately if the law is gutted.

About 20 million people are covered under Obamacare, the Department of Health and Human Services said earlier this year.